Hidetoshi and Rothman, 2008,Sacred Mathematics: Japanese Temple Geometry, pg 257
In a sector AOB of radius r, draw a small circle of radius x with center O. Draw the tangent to the small circle from the vertex B. As x is varied, the area S(x) of the black part of the figure will also vary. Show that S(x) is a maximum when x ≅ (293/744)r.
How is the area of the shaded region related to the radius of the circle?
Hidetoshi and Rothman, 2008,Sacred Mathematics: Japanese Temple Geometry, pg 120
Maximize y as a function of x assuming
BC = a is constant.
How is the area of the square related to the length of the vertical (blue) leg?
Hidetoshi and Rothman, 2008,Sacred Mathematics: Japanese Temple Geometry, pg 114
Given a rectangle ABCD with AB > BC, circle is inscribed such that it touches three sides of the rectangle, AB, AD, and DC. The diagonal BD intersects the circle at two points P and Q. Find PQ in terms of AB and BC.
How is the length of the (red) chord related to the vertical (blue) side of the rectangle?
JUST DESSERTS: Five Examples in Five Minutes
In a sector AOB of radius r, draw a small circle of radius x with center O. Draw the tangent to the small circle from the vertex B. As x is varied, the area S(x) of the black part of the figure will also vary. Show that S(x) is a maximum when x ≅ (293/744)r.
How is the area of the shaded region related to the radius of the circle?
Derivation of algebraic relationship:
A W-I-N modification of the problem above. How is the perimeter of the shaded region related to the radius of the circle?
Derivation of algebraic relationship:
Find x in terms of a when the area of the rhombus minus the area of the square is maximized
How is the area of the shaded region related to the length of the diagonal?
Derivation of algebraic relationship:
Maximize y as a function of x assuming
BC = a is constant.
How is the area of the square related to the length of the vertical (blue) leg?
Given a rectangle ABCD with AB > BC, circle is inscribed such that it touches three sides of the rectangle, AB, AD, and DC. The diagonal BD intersects the circle at two points P and Q. Find PQ in terms of AB and BC.
How is the length of the (red) chord related to the vertical (blue) side of the rectangle?
Derivation of algebraic relationship: